I believe that at least three related historic traditions harm the teaching of arithmetic in elementary school!

• There is a 2500-year-old prejudice against Pythagorean ideas due to the dominance of the philosopy of PLATONISM in university mathematics departments worldwide and in mainstream publishing. The Pythagorean approach is GENERATIVE, whereas the traditional method is AXIOMATIC, deriving from Plato's Academy in ancient Greece. But the GENERATIVE approach agrees with ALPHABETIC treatment of LANGUAGE, so ARITHMETIC HELPS LANGUAGE LEARNING and vice versa. But the AXIOMATIC is schizoid in SPLITTING "The 3 R's".

• There is also a prejudice against teaching HISTORY in MATHEMATICS and SCIENCE, both to STUDENTS and to TEACHERS. This prevents awareness of the above, as well as giving learning all the charm of the CIA or KGB.

• There is a further prejudice the notion that teaching one subject aids in teaching another. The GENERATIVE teaching of ARITHMETIC prepares for teaching about similar ideas in chemistry and physics and other subjects. But this prejudice motivates prospective teachers and professional teachers to ignore any suggestion that they could teach a subject in such a way as to help students learn other parallel and more advanced subjects. As a teacher of teachers, I've often heard the complaint, "Why should I take my time to present material which will be used by some other teacher?" Actors do something similar, called ënsemble-playing", and it helps the audience. And this would help the students.

The teaching of a MATHTIVITY such as PECKING ORDER corrects all three of the above defects in traditional teaching. And it pays a BONUS: As the PECKING ORDER REPERTORY shows, this LEARNING alone can, later, EXPAND into more than 30 SUBJECTS Of MATHEMATICS AND LOGIC.

Can you better this offer, anywhere else?